OneTaskBy Tim King · Updated
Newton's Cradle Simulator
Swing the Balls and Watch Momentum Transfer
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How the Newton's Cradle Simulator works
This Newton's cradle simulator shows momentum passing along the row. A row of steel balls hangs from a bar. One is lifted to the side and released; it strikes the row and the ball at the far end flies out while the rest stay still. Choose how many balls to lift and press Release, or drag any ball out with the mouse and let go. The other sliders change the number of balls, their size and the length of the strings.
Newton's cradle simulator: getting a good result
Newton's cradle is the desk toy that demonstrates conservation of momentum and of kinetic energy at the same time. When one ball hits the row, only one ball leaves the other end; lift two and two leave; lift three of five and three leave, with the middle ball swinging on both sides. Nothing else satisfies both conservation laws: if one ball came out at twice the speed, momentum would be right but the kinetic energy would double, and the universe does not allow that.
What the simulation does. Each ball is a rigid disc on an inextensible string, with restitution set to 1 so collisions are perfectly elastic and almost no air resistance, so a swing decays slowly the way a real cradle does. The engine resolves the collision of a moving ball with a touching row as a chain of near-instant impacts, which is how the impulse travels through a real cradle too: as a compression wave passing from ball to ball.
Lifting several. Set the slider to lift two, three or more, press Release, and count how many come out the far side. Try lifting more than half the balls: with three of five, the middle ball is in both groups and swings back and forth without ever stopping in the middle.
Kinetic energy. The panel sums half of mass times speed squared across all the balls every half second. Watch it at the bottom of a swing, when energy is all kinetic, and at the top, when it drops to zero as everything becomes potential energy. It creeps downward over time from the small air drag, exactly as a real cradle winds down.
Trying it by hand. Drag a ball with the mouse and release it from any height; drag two apart in opposite directions for a double collision. Stop resets every ball to hanging still. Everything runs in your browser using the Matter.js physics engine.
FAQ
Why does only one ball come out when one goes in?
It is the only outcome that conserves both momentum and kinetic energy. If two balls left at half the speed, momentum would match but the energy would be halved; if one left at double speed the energy would double. One ball at the same speed satisfies both laws.
What happens if I lift more than half the balls?
Set the slider to lift three of five and the middle ball belongs to both groups. It swings back and forth without ever resting in the middle, while the outer pairs alternate.
Why does the kinetic energy reading fall over time?
The simulation applies a very small air drag, so each swing loses a little energy and the cradle slowly winds down exactly as a real one does. The collisions themselves are perfectly elastic.
Can I set up my own collision?
Drag any ball out with the mouse and let it go from whatever height you like, or drag two balls apart in opposite directions for a double collision. Stop resets every ball to hanging still.
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